What to do when dementia patient wants to go home. She's thinking she has another home. She gets very upset and tries to leave the home.

If you can get her to taste the food she might take more than a taste.
“Here mom, does this taste too sweet, salty .., whatever you haven’t already tried.
Many elders will say they aren’t hungry but will eat food served to them. A straw is sometimes helpful (sometimes not so watch so see how she handles it).
Make sure you are watching her weight. Blood tests will show if her albumin is too low.
My aunt quits eating sometimes and will lose weight and then gain it all back. We can’t fill her up right now.
I don’t try to be overly controlling. Over the course of a year she will lose and gain back over 10 lbs.

I have alarms on all doors.  High tech ones (not expensive) that people use to stop kids from running and out and going to pool.   Low tech ones, Christmas bells hanging on door.  

My mom is social eater, will eat more when others do

Please understand that there is no reasoning with a person who has dementia. As we say here, their “brain is broken”. It no longer works. You can’t explain things to them. They don’t comprehend. All you can do is your best to keep her safe. It’s possible that may include sending her to a facility that has door alarms on locked doors. Also, my mother did not eat much when she got older. Offer many small meals and snacks during the day for her. And, if she hasn’t seen her doctor in a while, she needs to go.

This is very common, which is of no real help to you.

I'm not a med person, but perhaps she could benefit from some anti-anxiety meds.

Come up with a vague, calm response to her wanting to go home. She might not even know what that means anymore. People have said a lot of times they are even talking about their childhood homes. Figure out something you can distract her with when she gets like this. Is there something she likes to do? A snack, drink, tv show?